Dubois, Didier and Prade, Henri Znumbers as Generalized Probability Boxes. (2018) In: International Conference on Soft Methods in Probability and Statistics (SMPS 2018), 17 September 2018  21 September 2018 (Compiègne, France).

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Official URL: https://doi.org/10.1007/9783319975474_10
Abstract
This paper proposes a new approach to the notion of Znumber, i.e., a pair (A, B) of fuzzy sets modeling a probabilityqualified fuzzy statement, proposed by Zadeh. Originally, a Znumber is viewed as the fuzzy set of probability functions stemming from the flexible restriction of the probability of the fuzzy event A by the fuzzy interval B on the probability scale. However, a probabilityqualified statement represented by a Znumber fails to come down to the original fuzzy statement when the attached probability is 1. This representation also leads to complex calculations. It is shown that simpler representations can be proposed, that avoid these pitfalls, starting from the remark that when both fuzzy sets A and B forming the Znumber are crisp, the generated set of probabilities is representable by a special kind of belief function that corresponds to a probability box (pbox). Then two proposals are made to generalize this approach when the two sets are fuzzy. One idea is to consider a Znumber as a weighted family of crisp Znumbers, obtained by independent cuts of the two fuzzy sets, that can be averaged. In the other approach, a Znumber comes down to a pair of possibility distributions on the universe of A forming a generalized pbox. With our proposal, computation with Znumbers come down to uncertainty propagation with random intervals.
Item Type:  Conference or Workshop Item (Paper) 

Additional Information:  Thanks to Springer editor. This papers appears in volume 832 of Advances in Intelligent Systems and Computing book series ISSN: 21945357 ISBN 9783319975467 The original PDF is available at: https://link.springer.com/chapter/10.1007/9783319975474_10 
HAL Id:  hal02181922 
Audience (conference):  International conference proceedings 
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Institution:  Université de Toulouse > Institut National Polytechnique de Toulouse  INPT (FRANCE) French research institutions > Centre National de la Recherche Scientifique  CNRS (FRANCE) Université de Toulouse > Université Toulouse III  Paul Sabatier  UPS (FRANCE) Université de Toulouse > Université Toulouse  Jean Jaurès  UT2J (FRANCE) Université de Toulouse > Université Toulouse 1 Capitole  UT1 (FRANCE) 
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Deposited By:  IRIT IRIT 
Deposited On:  22 May 2019 13:03 
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